Extended Data Fig. 1: Supercritical coupling model.
From: Directive giant upconversion by supercritical bound states in the continuum
a, Top, oscillator scheme at the FW quasi-BIC, with depicted dispersion diagram of the FW-BIC formation near the avoided crossing point and with mismatched momentum with respect to the EIT occurring at the avoided crossing (dashed lines, frequencies; solid lines, linewidth). Bottom, the corresponding Hamiltonians (frequency and decay rate) at the ideal FW-BIC (kBIC), FW quasi-BIC (≃kBIC) and EIT (kEIT) points. b–d, Normalized intensity enhancements G/Gmax for both dark and bright modes (red and blue solid lines, respectively) compared with the corresponding single-resonance intensity enhancements (red and blue dashed lines) as a function of Qκ, for QR1 = 5 × 109, QR2 = 200, Qa = 5,000, with input frequency tuning with the dark (b), middle (c) and bright (d) frequency. e, Intensity-level ratio between the coupled dark mode Gdark at supercritical coupling and the single dark mode Gsingle-dark as a function of QR1/Qa and QR2/Qa: when QR1/Qa = 1, we find the critical coupling condition and the coupled dark mode has the same level of enhancement as the single dark mode. When QR2 ≫ Qa, there is no advantage (Gdark → Gsingle-dark) because the input channel is unfavourable. In the remaining region of parameters, Gdark ≫ Gsingle-dark.